Antiferromagnetism and single-particle properties in the two-dimensional half-filled Hubbard model: a non-linear sigma model approach

TL;DR

This paper presents a low-temperature non-linear sigma model approach to study antiferromagnetism and single-particle properties in the 2D half-filled Hubbard model, revealing the evolution from Slater to Mott-Hubbard antiferromagnetism and a finite-temperature metal-insulator transition.

Contribution

It introduces a novel low-temperature method based on a non-linear sigma model that captures both antiferromagnetic order and single-particle excitations in the Hubbard model.

Findings

At zero temperature, weak coupling shows Slater antiferromagnetism with small gaps.

Increasing U transitions the system to Mott-Hubbard antiferromagnetism with large gaps.

Finite temperature induces a metal-insulator transition between pseudogap and Mott insulator phases.

Abstract

We describe a low-temperature approach to the two-dimensional half-filled Hubbard model which allows us to study both antiferromagnetism and single-particle properties. This approach ignores amplitude fluctuations of the antiferromagnetic (AF) order parameter and is valid below a crossover temperature $T_X$ which marks the onset of AF short-range order. Directional fluctuations (spin waves) are described by a non-linear sigma model (NL$\sigma$M) that we derive from the Hubbard model. At zero temperature and weak coupling, our results are typical of a Slater antiferromagnet. The AF gap is exponentially small; there are well-defined Bogoliubov quasi-particles (QP's) (carrying most of the spectral weight) coexisting with a high-energy incoherent excitation background. As $U$ increases, the Slater antiferromagnet progressively becomes a Mott-Heisenberg antiferromagnet. The Bogoliubov bands evolve into Mott-Hubbard bands separated by a large AF gap. A significant fraction of spectral weight is transferred from the Bogoliubov QP's to incoherent excitations. At finite temperature, there is a metal-insulator transition between a pseudogap phase at weak coupling and a Mott-Hubbard insulator at strong coupling. Finally, we point out that our results straightforwardly translate to the half-filled attractive Hubbard model, where the ${\bf q}=(\pi,\pi)$ charge and ${\bf q}=0$ pairing fluctuations combine to form an order parameter with SO(3) symmetry.